Our analysis consisted of adaptive processes driven by mutation-specific evolutionary steps, i.e. in addition to the widely used point mutations, we introduced a minimal model of inversion mutations in double-stranded (digital) genomes.
This model has also revealed some consequences of the limits of simulations with point mutations.
We showed that, in addition to ruggedness due to epistatic interactions, the escape process can also depend on the interrelationships between the genotype space and the fitness landscape that are mediated by the type of mutation.
In particular, we showed that for inversion mutations, the graph-theoretical representation of accessible mutants displayed a complex topology, in comparison with the canonical genotype space constructed with point mutations.
By definition, the node degree of the graph of mutations is the number of accessible mutants.
In the case of inversions this number is no longer constant over the node set—as in the case of point mutations—but varies depending on the specific sequence composition.
Therefore, although it is correct that we can generate genotypic space through point mutations, that does not (strictly) imply that evolutionary paths in the fitness landscape have to be solely through point mutations.
In this sense, the inversion mutations allowed us to reveal new topological properties of the interconnection between genotypes through what we have defined as mutational networks.
Indeed, it is this mutational network that mediates the interconnection between genotype space and the adaptive dynamics in the fitness landscape.
The mutational network can be translated as a fitness network when the fitness values of each mutant genotype are included.
Thus, revealing the directions of possible evolutionary paths.
Let us remark that graph theory is a framework used in various models of evolution (see for example Refs. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}) and has been advantageous in analysis that use the Kauffman model, such as [12]}, [13]}, [14]}, [15]}, [16]}, [17]}.
However, most of these graph representations for mutations and fitness landscapes are isomorphic to the (hypercubic) genotype space, whereas our definition of mutational and fitness networks are not necessarily isomorphic to the genotype space.
Moreover, we showed that for fitness networks generated by inversions, there are more mutational pathways between genotypes compared to point mutations.
Therefore, for inversion mutations, at each step an evolutionary process can potentially explore more accessible mutants, than the “classical” estimation
\((|\mathcal {A}_{\mathcal {L}}|-1)N\) , for any alphabet \(\mathcal {A}_{\mathcal {L}},\forall \mathcal {L}\in \lbrace 2n : n \in \mathbb {N}\rbrace \) , with size \(|A_{\mathcal {L}}|=2n\) .
In this sense, our work can straightforwardly complement the results reported in [18]}, for \(|\mathcal {A}_{\mathcal {L}}|>2\)  with point mutations.
The main message here is that in addition to the well-known utility of the fitness landscape metaphor, its topographic properties (due to epistasis) are not sufficient for modelling the escape from local peaks, and additional information should be included via the topology of mutational networks and fitness networks.
This information can be useful to predict evolutionary trajectories in fitness landscapes [19]}, [20]}, [21]}, [22]}, [23]}, [24]}.
